There are various methods for measuring the moment of inertia of a motor , each suitable for different motors, and the measurement accuracy varies. In previous posts, we introduced the calculation method and the single-wire method for measuring moment of inertia. Today, we'll discuss three other commonly used methods: the double-wire method, the assisted pendulum method, and the no-load deceleration method.
Double steel wire test method
Compared with the single-wire method, the double-wire method has the advantages of low testing cost and high accuracy, so it is widely used in practice, but the installation is more complicated.
● Rotor suspension requirements
The rotor under test is suspended vertically from a support using two steel wires of equal length, ensuring that the rotor's axis remains vertical. The wire length should generally not exceed 2 meters to minimize changes in wire length due to torsional oscillation. For ease of installation, the distance between the upper and lower ends of the wires can be unequal. The selection principle for the wire diameter is the same as for the single-wire method.
●Test Procedure
(1) After rotating the rotor from a stationary state to an angle of less than 10°, release the hand, allowing the torque of the steel wire to freely rotate and swing back and forth. Measure several [units/points] using the same method as the single-wire method.
The average value T of the oscillation period.
(2) Calculate the moment of inertia J (kg·m2) of the test rotor using formula (1).
In formula (1):
T — the time (s) of one oscillation cycle;
m — rotor mass (kg);
g—acceleration due to gravity, g=9.8m/s2;
a——half the distance between the upper ends of the two steel wires (m);
b——half the distance between the lower ends of the two steel wires (m);
L—Vertical distance between the two ends of the steel wire (m).
Auxiliary pendulum swing measurement method
For motor rotors that are already assembled into a complete machine or for larger rotors, the moment of inertia can be determined using an auxiliary pendulum swing test method. This method is relatively easy to operate, but its accuracy is poor. To verify the accuracy of the test, the moment of inertia of a rotor can be repeatedly measured using pendulums of different masses, and the more stable value can be taken as the test result.
●Requirements for the motor
The rotor is installed in the motor in the normal manner. To ensure smooth rotor rotation, rolling bearings must be used and properly lubricated. If the motor uses sliding bearings, the rotor must be mounted separately on a balancing machine. For motors equipped with brushes, all brushes must be lifted during testing.
● Requirements for the fabrication and installation of the auxiliary pendulum
The auxiliary pendulum consists of a pendulum and a connecting rod. The pendulum is cylindrical, and its mass should be as light as possible while still being able to overcome the moment of inertia of the rotor of the motor under test. Generally, its moment of inertia is designed to be no more than 10% of the moment of inertia of the rotor of the motor under test.
The connecting rod should be as lightweight as possible, preferably made of wood. Its length should be selected according to the size of the motor. For motors above 10kW, the oscillation period should be controlled within 3-8s; for motors of 1-10kW, the oscillation period should be controlled within 1-3s.
Securely mount the auxiliary pendulum to the shaft extension so that it hangs down naturally and its axis coincides with the vertical line.
● Actual measurement steps
(1) Swing the pendulum until the angle between it and the vertical is within 15°. Release the pendulum and let it swing freely like a pendulum. Record the time taken for 2 to 3 swing cycles and calculate the average value T(s) of one cycle.
(2) Calculate the moment of inertia J (kg·m2) of the rotor. Assume that the mass of the connecting rod is very small and can be ignored. Use equation (2) to calculate the moment of inertia of the rotor.
In formula (2)
Ma — Mass of the pendulum (kg);
a——Distance from the center of gravity of the pendulum to the axis of the motor (m);
T – the average value over one period (s);
g—acceleration due to gravity, g=9.8m/s2.
No-load deceleration method
This method is applicable to assembled motors of 100kW and above. Its advantages are that no auxiliary devices are required, and the measurement can be performed regardless of the type of bearing used in the motor, making it more suitable for larger motors. The disadvantage is that the mechanical losses of the motor under test must be measured beforehand, which requires certain instruments, equipment, and testing capabilities.
●Preparatory work before the experiment
Before the test, the motor under test should be run idle for a certain period of time to allow its mechanical loss to reach a stable state, and the mechanical loss Pm of the motor should be measured.
●Test Procedures and Precautions
(1) Use methods such as increasing the power supply frequency (for AC motors), increasing the voltage, or reducing the excitation (for DC motors) or other mechanical drives to make the speed of the tested motor exceed 1.1 times its rated value. Then, cut off the power supply or disconnect the prime mover and let the motor decelerate and stop on its own.
(2) During the process of the motor speed decreasing from 1.1 times to 0.98 times the rated speed, or from 1.05 times to 0.9 times the rated speed, accurately measure the speed difference Δn (r/nin) and the time Δt (s) taken for Δn to change.
To accurately read the motor speed, it is best to use a tachometer that allows direct observation of the continuous decrease in speed, such as a centrifugal pointer tachometer.
(3) Using the data obtained above, the moment of inertia J (kg·m2) of the rotor of the tested motor is obtained by formula (3).
In formula (3):
Pm — Mechanical loss (W) of the tested motor;
ns — synchronous speed (r/min) of the tested motor.
(4) When the tested motor cannot exceed the rated speed, the test can be performed between 1 and 0.8 times the rated speed. In this case, Pm should be the mechanical loss value at 0.9 times the rated speed.
